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We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution. Building on these results, the variational analysis can be completed ensuring existence and uniqueness of the optimum. The latter can then be computed by standard, efficientarXiv:1301.6658v1 fatcat:j5h4d3hgrfat3nxdghjqbjd7pi